Question

Quantitative Reasoning | Module 10: Homework133 Allegra is starting a small record label and has secured start-up funding in the form of an interest only loan for s90,000, which hasan APR of 9.9% compounded monthly. Since the loan is interest only, she will not pay off any of the balance of the loan until it comes to term at the end of eight years. Instead, she will simply pay the monthly interest owed on the loan amount of $90,000. 4. How much will this monthly interest payment be? At the end of eight years, Allegra will need to repay the entire $90,000 all at once. In order to prepare for this repayment, she has set up a separate savings account with an APR of 4.05%. (Such an account is sometimes referred to as a sinking fund.) How much must she deposit into this account each month in order to have $90,000 saved in eight years? What are Allegras total monthly expenses due to these two payments?

Answer 1

4)

monthly interest = APR/12 = 9.9/12 = 0.825% = 0.00825

monthly interest payment = monthly interest *( loan amount) = 0.00825*90000 = 742.5

b)

APR of savings account = 4.05%

monthly APR, r = 4.05/12 = 0.3375% = 0.003375

no. of years = 8

no. of months, n = no. of years*12 = 8*12 = 96

monthly deposit = Loan amount /FVIFA

FVIFA = future value interest rate factor of annuity = ((1+r)ⁿ-1)/(r) = ((1.003375)⁹⁶-1)/0.003375 = 113.1535547

Monthly deposit = 90,000/113.1535547 = 795.379343

c) total monthly expense = monthly interest payment + monthly deposit = 742.5 + 795.379343 = 1537.87934 or 1537.88 ( rounding off to 2 decimal places)